You\'re a systems engineer at Dtale airlines....I just can\'t seem to get excel

Question

You're a systems engineer at Dtale airlines....I just can't seem to get excel equation right.

Problem 8 You're a systems engineer at Stale Air airlines charged with helping the airline to overbook flights. You realize that a certain percentage of ticketed passengers will cancel at the last minute. Therefore, to avoid empty seats, the airline wants to sell more tickets than there are seats, hoping that just about the right number of passengers show up. You assume that the no- show rate is 10% and assume that passengers choose to show up independently of each other For a flight with 200 seats, the airline wants to see how sensitive various probabilities are to the number of tickets it issues. a. Calculate the probability that more than 205 passengers show up for the flight. b. Calculate the probability that more than 200 passengers show up. c. Calculate the probability that at least 195 passengers show up. d. Calculate the probability that at least 190 passengers show up. You're going to suggest that the airline issues a minimum of 205 tickets for the flight, and as many as 230, with all possibilities in between. Use Excel to calculate the four probabilities ina-d for each of the ticket allotment possibilities (be thoughtful in setting up the parameters so that you do as little manual entering as possible -this thought on setting it up properly) about how many tickets to issue. (adapted from [Albright et al. 2011]) problem can be answered quickly with some . Use the outout of this exercise to make an informed decision

Explanation / Answer

Let X be the random variable that number of passengers show up for the flight.

X ~ Binomial (n = 230, p = 0.9)

a) Calculate the probability that more than 205 passengers show up for the flight.

That is here we have to find P(X > 205).

EXCEL syntax is,

=1 - BINOMDIST(number_s, trials, probability_s, cumulative)

where number_s = 205

trials = 230

probability_s = 90% = 0.9

cumulative = TRUE

P(X > 205) = 0.6390

b) Calculate the probability that more than 200 passengers show up.

Here we have to find P(X > 200)

EXCEL syntax :

=1 - BINOMDIST(number_s, trials, probability_s, cumulative)

number_s = 200

trials = 230

probability_s = 0.9

cumulative = true

P(X>200) = 0.9197

c) Calculate the probability that at least 195 passangers show up.

That is here we have to calculate P(X >=195)

P(X>=195) = 1 - P(X<194)

EXCEL syntax for P(X<194) is,

=BINOMDIST(number_s, trials, probability_s,cumulative)

P(X<194) = 0.0048

P(X>=195) = 1 - 0.0048 = 0.9952

d) Calculate the probability that at least 190 passengers show up.

We have to find P(X>=190).

EXCEL syntax :

=1 - BINOMDIST(number_s, trials, probability_s,cumulative)

P(X>=190) = 0.9998

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